From DDOWiki:
Ninja Training: While you are centered, you can use your Dexterity modifier for damage with piercing and slashing weapons. You also gain a chance based on your Dexterity score to throw an extra shuriken per attack.
AP Cost: 2 Level: 3 Progression: 5 Requires: Monk Level 3, Ninja Training (Rank 1)
Ninja Training II, required for taking Shadow Veil, seems to be affecting bows. Unfortunately, it overwrites bow strength (at least in the display portion) even if your strength is higher than your dex. I had a +5 bonus from dex and can boost to a +11 bonus from strength. At least as far as the display goes it shows +5 (from Dex) on the damage portion of the bow. Tests on the target dummy seemed to indicate this was indeed true though it's hard to say with any certainty without extensive testing.

If this is the case then Ninja Spy is a tough choice for many monkchers. With 3 stats to raise if you're taking Overwhelming Critical, Combat Archery, and 10k Stars you're likely going to have a much higher boosted strength than dex (probably in the +5-6 range). That means that under the current system you have to give up 5-6 damage per arrow in order to take Shadow Veil. I'm sure that Ninja Training II wasn't intended to ever lower your damage output though so hopefully this is just a display bug or it gets fixed.